The Guiding Wave
Waves
The nature of the correction process that maintains the average speed and direction of light particles constant becomes apparent if we make a second tiny hole in the screen about 2 mm away from the first. Again, at very low intensities, individual arrival events can be detected. And again the spots arrive at random times and positions. However, as time goes on, a pattern of stationary waves appears instead of a smooth distribution with a single peak. This is a surprising way for discrete particles to behave.
We might validate this surprise by scaling up the experiment to use bullets on a firing range instead of photons in a lab. The behavior of individual bullets is much better understood than the behavior of single photons. If we were to scale up in this way, we would find that the bullets from each hole build up the same smooth, single-peaked distribution as before. The two distributions would superimpose to produce a smooth final distribution with a slight dip in the middle due tof the spacing between the holes. So, why do we not get a distribution like this when photons pass through two holes, becauset light is made up of individual particles comparable to bullets?
Instead we get a wave pattern like that forming in a harbor if waves enter through two different gaps in the breakwater. That situation provides an alternative scaled-up version of the two apertures in the screen. A short distance inside the breakwater, waves coming through one passage meet waves coming through the other. As a result, a stationary wave pattern forms in the harbor water. Where incoming crests meet, a standing appears, rising to a maximum. Where troughs meet, the stationary wave that is formed descends to a minimum. In between, there is a smooth transition between wave maxima and minima, which is a transition in potential energy, high at the peaks, low at the troughs. A surfer can gain speed by sliding from peak to trough, exchanging potential energy for kinetic energy.
How can photon particles (or electrons) passing through two small holes in a screen produce a standing wave pattern like waves in water? For such particles to be drawn into a wave pattern, they must be steered in some way, because they are certainly not waves. We are, in fact familiar with the way the kinetic energy of moving electrons can be steered by using the energy of electrodes at an electrical potential..This steering of kinetic energy by potential energy was used in television displays to paint a picture, before flat panel displays came in. I suggest that a comparable steering of both photons and electrons is active in producing the pattern on the screen beyond the twin holes. The electrons or photons are steered into a wave pattern by a standing wave of potential energy possessing the pattern that is seen.
As the photons with kinetic emerge from the holes, they encounter a standing wave of potential energy. Depending on their speed and angle, are steered towards the peaks or valleys of the wave. We are seeing a transformation of energy comparable to that occurring when the potential energy of a pendulum is transformed into kinetic energy, although there is a dual energy momentum transfer. The energetic change in the photon paths is produced by a standing wave pattern of potential energy. To be present in the form of a stationary wave, the potential energy wave itself will be the result of an initial moving potential energy wave that is split into two components by the holes in the screen. Like the waves in the harbor coming through two different entrances, the two potential energy waves emerging from the holes combine into standing waves of potential energy in the way water waves do.
For the right wave splitting to occur, an energy wave arriving at the holes must be aligned along the path of the photons. However, we are unaware of its presence until it is split by the two holes to produce secondary waves that recombine as standing waves. Then the presence of a hidden energy wave is revealed by the pattern of photons or electrons that surf over these wave on to the screen.
The invisible wave that has been induced to reveal itself through wave interference is my candidate for the mechanism that, in the absence of a perforated screen, steers deviant photons back to a straight path and a constant speed of light. I think the most likely source of the potential energy wave is the energy within the interstices of the latttice of of spacetime quanta.
I should point out that an alternative solution has been put forward. It proposes that opening the second hole causes the photons or electrons to become waves, which then interact to produce an interference pattern. I do not find this argument persuasive. Waves and particles are exclusive categories of phenomena. A wave is continuous in space, a particle is a discrete event. The properties of the two are not only different but mutually exclusive. Logically, an object cannot be both at the same time. It is more reasonable to suppose that the pattern of electrons or photons comes from the interaction of the kinetic energy of the particles with the potential energy of a wave. Furthermore, given the randomizing properties of the spacetime lattice, some pattern of energy interchange such as this is clearly necessary to restrain particles within the lattice to a straight path and provide for conservation of energy-momentum and constancy of average velocity. A waveform that could do this would accompany particles like photons and electrons but would be distinct from them.
Interstitial Energy
An available source of energy for such a waveform is in the interstices of the spacetime lattice. The lattice itself by the regularity it imposes on the interstices holding that energy brings a component of locality to what would otherwise be an undisturbed region of eternity. I think a waveform that can be produced in this region will be spatial and pseudo-stationary, because time varying waveforms are found in the non-contiguous spacetime lattice that can form space-time relationships by virtue of its time structure. The interstitial energy is not discrete but continuous. Spatial waveforms can appear in it by subtraction of energy from individual interstices in a regular spatial pattern. In this way a local patch of stationary spatial waveform can appear. The pseudo-stationary aspect arises because I assume it is activated by a particle possessing kinetic energy and moves along with that particle, maintaining energy-momentum conservation and minimization laws.
In the production of light, the waveform would appear when a photon is released by an electron. The drop in potential energy of the electron is balanced by the kinetic energy of the photon. I assume the appearance of the kinetic energy of the photon in the lattice releases a standing wave of potential energy in the interstices of the lattice that restores the net energy in the region of particle movement through the lattice back to its standing level. The energy of such a wave is proportional to its frequency, which has previously been made a property of the particle without an account of how a particle can become a wave, the conversion of particle energy into wave energy, or the possible appearance of particle-wave energy.
As the photon makes random jumps through the lattice, its kinetic energy fluctuates. To compensate for this, an energy exchange takes place between the energy of the photon and the energy of the wave, which constantly moves the net energy in the lattice back towards its standing level. When the photon vanishes, as a result of capture by an electron, the interstitial wave instantly vanishes also.
The characteristics of the interstitial waveform, which can be measured in the twin hole and other experiments, are well known. The number of waves per meter corresponds to the energy of the photon divided by the reduced Planck constant. The angular frequency corresponds to the momentum of the photon multiplied by that constant. A similar type of relationship holds for matter particles as well. This enables the dependence of the interstitial waveform on momentum to be demonstrated. The method is to repeat the twin hole experiment with electrons but add an instrument that detects when an electron passes through one of the holes.
A light is shone on the holes so that an emerging electron will be hit by a photon. When the photon is reflected, signaling contact with an electron, it will be detected by a photomultiplier. In the act of moving through one of the holes, the electron will be betrayed by a brief flash of light. We will know which hole it came through. The experiment was originally conceived as a means of understanding how a particle managed the impossible trick of turning into a wave. Followers of the concept of wave-particle duality wanted to know how an electron traveling towards one hole could find out whether a second hole nearby was closed or open. In the first case it would go through just one hole as particle. In the second it would turn into a wave and pass through both holes, simultaneously. It was thought that the experiment would throw some light on this amazing performance, and suggest how the electron discovered the presence or otherwise of a second hole..
Unfortunately, when the passage of a particle through one of the holes was detected, the wave pattern disappeared, to be replaced by the smooth distribution expected of particles passing through a single hole. This result caused extensive metaphysical speculation, leading to the pronouncement that Nature conspires to keep humanity ignorant of what it is up to when light passes through two holes in a screen. The explanation is more prosaic. When the photon hits the electron, an exchange of momentum takes place. The wave number of its associated travelling wave changes. It no longer matches the wave number of the standing wave of potential emerging from the second hole.Two different waves do not interfere with each other to produce a regular pattern of standing waves.
The interference pattern that appears in the twin-hole experiment with monochromatic light arises from a potential energy waveform that has a measurable wavelength. Hitherto, this wavelength has been treated as if it were an attribute of a particle of light or an elecctron. This led to the questionable logic of wave-particle duality of matter and radiation. Instead, the waveform is an attribute of the interstitial energy of the lattice in its reaction to the random motions that the spacetime lattice imposes on particles as they skip through spacetime quanta.
The mathematics of quantum mechanics remain intact. The concept of a distributed probability waveform that accurately forecasts the future state of a system of particles remains. However, these probabilities do not determine the behavior of particles any more than the weather forecast determines the weather. It takes real waves to do that. For a particle moving through spacetime, waves in the energy of eternity trapped in the interstices of spacetime offer a source of the wave action.
Why do we have to go to individual particles to see interference patterns associated with moving objects? The experiment to test which hole the particle passes through gives an indication. In a composite body the particles are jostling each other, smearing out their energy-momenta, so the interference wave does not appear. But this does not mean it is not there. It is the interference pattern not the wave that disappears. Its steering function is still carried out, but the presence of multiple wavelengths smears out any attempt to produce an interference pattern.
The interstitial energy within the spacetime lattice is eternal (atemporal and aspatial). It has no locality within itself, but it has an external locality imposed on it by the spacetime lattice it encloses (or that encloses it: the embrace is mutual). The interstitial energy senses a disturbance caused by kinetic energy within its vicinity and acts to conserve energy and momentum. It sets up a waveform of potential energy that smooths out deviations in the path of a kinetic energy particle. When there is a composite body with kinetic energy moving in a potential energy field (a rock thrown up in the air), the waveforms steering individual particles produce a combined result that gives rise to the principle of least action.
This in itself provides the foundation for of the guiding wave’s action, as is described in the next section.